Combined Stresses

1
Combined Stresses

• Machine components are subjected to a variety of
  loads.
• Normal and shear stresses affect materials
  differently.
• These stresses must be combined into a resultant
  state of stress.

• Torsion
• Bending

• Normal
• Direct shear

2
General Bi-axial Stress
sy
Sign convention s tension t rotates
clockwise
3
Example

• Calculate the stress components at point A of the
  shaft shown.

4
State of Stress

• By rotating the reference frame, the individual
  stress values change.
• The state of stress remains the same.

sx

• Some configurations are more convenient.

5
Force Components

• A force can be broken into x y components

• Components vary with the reference axes, but
  resultant force is the same.
• Stress is similar.

6
Transforming Stress Components

• Create a sand t axes
• Plot (sx, txy) and (sy, tyx)

t
txy
sy
s
sx
tyx
7
Mohrs Circle

• Use the two points to create a circle
• Mohrs Circle

8
Mohrs Circle

• Any points on the circle represent stress
  components.

9
Example

• Construct a Mohrs Circle for point A of the
  shaft shown.

10
Principle Stresses

• Orient reference frame until normal stress on one
  face becomes a maximum (s1).
• Stress on orthogonal face will be a minimum (s2).
• Shear stresses are eliminated

11
Principle Stresses

• Maximum
• Minimum
• Angle

12
Example

• Determine the principle stresses for point A of
  the shaft shown

13
Maximum Shear Stress

• Orient reference frame until shear stress becomes
  a maximum (tmax).

• Notice that an equal normal stress (savg) is
  present on both faces.

14
Maximum Shear Stress

• Max Shear
• Avg Normal
• Angle

15
Example

• Determine the maximum shear stress for point A of
  the shaft shown